About the Q * V implementation:
I can't use it, because it behaves like Q is inversed for my case.
Please, make sure the convention you choose matches the one most of people use.
(Already scanned 3 links, all pointing to the way I need).

Moreover, I expected the implementation not to be straightforward (Q*V*inv(Q)), but use the knowledge of V.w = 0.
In GLSL my transform function looks like this: